Theoretical calculations on half-lives of spontaneous one-proton radioactivity

Hanlin Wang; Zhen Wang; Zhongzhou Ren

arxiv: 2606.17785 · v1 · pith:22YJCP2Inew · submitted 2026-06-16 · ⚛️ nucl-th

Theoretical calculations on half-lives of spontaneous one-proton radioactivity

Hanlin Wang , Zhen Wang , Zhongzhou Ren This is my paper

Pith reviewed 2026-06-26 22:07 UTC · model grok-4.3

classification ⚛️ nucl-th

keywords one-proton radioactivityhalf-livesdeformed Woods-Saxon potentialGamow state theoryproton drip linequantum tunnelingnuclear decay

0 comments

The pith

Calculations with deformed Woods-Saxon potentials and microscopic Gamow theory produce half-lives for proton emitters with 50 < Z < 84 plus predictions for 30 < Z < 50.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs the daughter-proton potential from a deformed Woods-Saxon term, spin-orbit potential, and expanded Coulomb potential. Half-lives are then obtained through the quantum tunneling model and microscopic Gamow state theory for observed proton emitters. Comparisons to measured values allow assessment of how the results depend on decay energy and spectroscopic factors. Predictions are extended to possible lighter emitters in the fpg shell. The compiled dataset covers both the experimentally confirmed range 50 < Z < 84 and the theoretically predicted range 30 < Z < 50.

Core claim

Using deformed Woods-Saxon potential, spin-orbit potential, and expanded Coulomb potential to construct the daughter-proton potential, the half-life data of various proton emitters are systematically calculated based on the quantum tunneling model and the microscopic Gamow state theory. By using nuclear data from different sources and comparing them with the measurements, the dependence of proton emission on decay energy and spectroscopic factors is evaluated. Additionally, based on previous observations, the half-life of the possibly lighter proton emitter in the fpg-shell below has been theoretically predicted. Our results are compiled into a comprehensive dataset of half-lives for both ex

What carries the argument

Deformed Woods-Saxon potential combined with microscopic Gamow state theory, which supplies the potential barrier and the quantum tunneling rate for the emitted proton.

If this is right

Half-lives show clear dependence on both decay energy and the chosen spectroscopic factors.
A ready dataset exists for use in planning experiments near the proton drip line.
Theoretical half-lives are supplied for possible new emitters with 30 < Z < 50.
The same framework can be reapplied when new nuclear data update the input parameters.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the predictions hold, targeted experiments could confirm new proton emitters by searching for the calculated decay energies and lifetimes.
Systematic comparison of these results with alternative barrier models would isolate the role of nuclear deformation in the tunneling rates.
The dataset format could be reused to tabulate half-lives once two-proton or cluster emission data become available for the same mass region.

Load-bearing premise

Spectroscopic factors and the specific parametrization of the deformed Woods-Saxon potential taken from existing nuclear data sources remain accurate across the full Z range examined.

What would settle it

An experimental half-life measurement for any predicted emitter in the 30 < Z < 50 range that differs by more than an order of magnitude from the calculated value.

read the original abstract

Research on the unstable nuclei beyond the nucleon drip line is an important method to study the nuclear interaction and structure in the extremely neutron-deficient or rich systems. Various nuclides beyond the proton drip line mainly decay through spontaneous one-proton emission. Using deformed Woods-Saxon potential, spin-orbit potential, and expanded Coulomb potential to construct the daughter-proton potential, the half-life data of various proton emitters are systematically calculated based on the quantum tunneling model and the microscopic Gamow state theory. By using nuclear data from different sources and comparing them with the measurements, the dependence of proton emission on decay energy and spectroscopic factors is evaluated. Additionally, based on previous observations, the half-life of the possibly lighter proton emitter in the fpg-shell below has been theoretically predicted. Our results are compiled into a comprehensive dataset of half-lives for both experimentally confirmed emitters (50 < Z < 84) and theoretically predicted emitters (30 < Z < 50), providing a useful reference for future experimental investigations related to the proton drip line. The datasets presented in this paper, including our results of calculation, are openly available at https://www.doi.org/10.57760/sciencedb.27551.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

A straightforward compilation of proton-emitter half-lives using standard deformed potentials and Gamow tunneling, with an open dataset but no new formalism or independent validation of inputs.

read the letter

The paper runs a systematic set of half-life calculations for one-proton emitters in the range 50 < Z < 84 and extends predictions down to 30 < Z < 50. It uses the usual deformed Woods-Saxon plus spin-orbit plus Coulomb potential inside the microscopic Gamow formalism, pulls spectroscopic factors and parameters from existing nuclear data tables, and releases the full numerical results at a DOI link.

What it does cleanly is collect everything into one reference table and show the expected strong dependence on decay energy and spectroscopic factor by direct comparison to measured cases. The open data release is the most practical part; experimental groups planning drip-line runs can pull numbers without re-deriving the potentials themselves.

The main limitation is that the potential parameters and spectroscopic factors are taken from external sources with no fresh cross-check or uncertainty propagation shown for the lighter nuclei. If those inputs were already adjusted to the higher-Z data, the lighter predictions are extrapolations whose accuracy rests on untested transferability. The abstract notes comparisons with experiment but gives no fit statistics or error bars, so a reader cannot judge how much the results are tuned versus predicted.

This is useful reference material for experimental nuclear physicists who need tabulated half-lives near the proton drip line. Theorists looking for new methods or first-principles insight will not find it here. The calculations are standard and the dataset is reproducible in principle, so the work is worth sending to referees who can check the input choices and the numerical implementation.

Referee Report

2 major / 1 minor

Summary. The manuscript claims to construct daughter-proton potentials from deformed Woods-Saxon, spin-orbit, and expanded Coulomb terms, then compute one-proton emission half-lives for confirmed emitters (50 < Z < 84) via the quantum tunneling model and microscopic Gamow state theory. Nuclear data from multiple sources are used to evaluate the dependence of the results on decay energy and spectroscopic factors through comparison with measurements; predictions are also given for lighter emitters (30 < Z < 50), and all calculated values are compiled into an openly available dataset.

Significance. If the adopted potential parameters and spectroscopic factors can be shown to have been chosen independently of the half-lives being calculated, the work supplies a systematic reference dataset for proton-drip-line studies together with open data, which is a clear strength for reproducibility.

major comments (2)

[Abstract and §2] Abstract and §2 (potential construction): the text states that deformed Woods-Saxon parameters and spectroscopic factors are taken from nuclear data sources, yet provides no explicit statement or table demonstrating that these inputs were fixed without reference to the same half-life measurements used for validation; this leaves the transferability of the parametrization to 30 < Z < 50 predictions unverified and risks circularity in the reported comparisons.
[Results section] Results section on comparison with experiment: no quantitative measures (error bars on calculated half-lives, χ^{2} values, or reproduction statistics within stated uncertainties) are reported for the agreement between Gamow-tunneling results and measured half-lives, which is required to substantiate the claim that the microscopic formalism reliably reproduces the data.

minor comments (1)

[Dataset availability statement] The open-data DOI is a positive feature; the deposited files should include the precise numerical values of all potential parameters and spectroscopic factors used for each nucleus to allow independent reproduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and constructive comments on our manuscript. We address each major comment below, indicating the revisions we plan to implement.

read point-by-point responses

Referee: [Abstract and §2] Abstract and §2 (potential construction): the text states that deformed Woods-Saxon parameters and spectroscopic factors are taken from nuclear data sources, yet provides no explicit statement or table demonstrating that these inputs were fixed without reference to the same half-life measurements used for validation; this leaves the transferability of the parametrization to 30 < Z < 50 predictions unverified and risks circularity in the reported comparisons.

Authors: The deformed Woods-Saxon, spin-orbit, and Coulomb potential parameters, together with the spectroscopic factors, are taken from standard nuclear data compilations and global fits (e.g., to binding energies, radii, and scattering data) that predate and are independent of the proton-emission half-life measurements used for comparison. To make this independence explicit and to strengthen the justification for the 30 < Z < 50 predictions, we will add a dedicated paragraph and table in §2 that lists each source and confirms its basis in non-decay observables. This revision directly addresses the concern about circularity and transferability. revision: yes
Referee: [Results section] Results section on comparison with experiment: no quantitative measures (error bars on calculated half-lives, χ^{2} values, or reproduction statistics within stated uncertainties) are reported for the agreement between Gamow-tunneling results and measured half-lives, which is required to substantiate the claim that the microscopic formalism reliably reproduces the data.

Authors: We agree that quantitative measures are needed to substantiate the agreement. In the revised manuscript we will add error bars on the calculated half-lives (propagated from uncertainties in Q-values and spectroscopic factors), report χ² values for the full set of confirmed emitters, and include reproduction statistics (e.g., percentage of cases within factors of 2 and 10). These additions will be placed in the Results section and will support the reliability claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity; inputs drawn from external nuclear data sources with explicit comparison to measurements

full rationale

The derivation relies on deformed Woods-Saxon parameters, spin-orbit terms, Coulomb potential, and spectroscopic factors taken from independent nuclear data compilations. Half-lives are computed via the microscopic Gamow formalism and then compared to experimental values to assess dependence on decay energy and spectroscopic factors. The lighter-Z predictions (30 < Z < 50) are extrapolations based on the same external parametrization rather than refits to the target half-lives themselves. No equation or section reduces a claimed prediction to a fitted quantity by construction, and no self-citation chain supplies the load-bearing uniqueness or ansatz. The work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The calculation rests on standard nuclear potentials whose parameters are drawn from external data sources; no new entities are introduced.

free parameters (2)

deformed Woods-Saxon parameters
Standard parameters taken from nuclear data sources; their specific values for each emitter are not listed in the abstract.
spectroscopic factors
Evaluated from nuclear data; dependence on these factors is stated as part of the analysis.

axioms (2)

domain assumption Quantum tunneling through the constructed daughter-proton potential governs the decay rate
Invoked when the half-life is obtained from the Gamow state theory.
domain assumption Deformed Woods-Saxon plus spin-orbit plus expanded Coulomb potentials adequately represent the proton-nucleus interaction
Stated as the method used to construct the potential.

pith-pipeline@v0.9.1-grok · 5738 in / 1408 out tokens · 25606 ms · 2026-06-26T22:07:12.750609+00:00 · methodology

discussion (0)

Reference graph

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d!d𝑟!+𝑉#$%&,((𝑟)+𝑉)*$&,((𝑟)+ℏ!2𝑚

and theoretically predicted ones (50 < Z < 84). Section 4 summarizes the conclusions of this work. 2 Theoretical Model for Deformed One-Proton Radioactivity 2.1 Proton-Daughter Nucleus Two-Body Interaction and Gamow States Spontaneous one-proton radioactivity occurs in proton-unbound nuclei beyond the proton drip line, where the emitted proton tunnels thr...

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Table 1 Experimental data of various proton emitters, where the orbital is occupied in the spherical limit. 𝑄@A4 and 𝑄BC0D represent the decay energies derived from experiments (obtained from NNDC and AME 2020[3,40,41], except for values explicitly marked otherwise) and the Finite-Range Droplet Model (FRDM) theory[39], respectively. 𝛽!,. denote the deform...

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4 The difference between this work and other theoretical methods (including an analytic semiclassical solution[11] and the new Geiger-Nuttall law[44])

Fig. 4 The difference between this work and other theoretical methods (including an analytic semiclassical solution[11] and the new Geiger-Nuttall law[44]). The horizontal axis denotes the nucleon number of the parent nucleus, while the vertical axis illustrates the difference between the logarithms of the calculated and experimental half-lives. 3.2 Theor...

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